Advertisements
Advertisements
प्रश्न
Construct the truth table of the following:
[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]
Advertisements
उत्तर
| p | q | r | p∧q | (p∧q) ∨ r | ∼r | ∼r ∨ (p∧q) | [(p∧q) ∨ r] ∧ [∼r ∨ (p∧q)] |
| T | T | T | T | T | F | T | T |
| T | T | F | T | T | T | T | T |
| T | F | T | F | T | F | F | F |
| T | F | F | F | F | T | T | F |
| F | T | T | F | T | F | F | F |
| F | T | F | F | F | T | T | F |
| F | F | T | F | T | F | F | F |
| F | F | F | F | F | T | T | F |
APPEARS IN
संबंधित प्रश्न
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.
[~(~p ∧ ~q)] v q
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Write the following compound statement symbolically.
The angle is right angle if and only if it is of measure 90°.
Construct the truth table of the following statement pattern.
(p ∧ ∼q) ↔ (p → q)
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
(∼ p → ∼ q) ∧ (∼ q → ∼ p)
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Construct the truth table of the following:
p → (q → p)
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Write the negation of the following statement.
All men are animals.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the truth value of the negation of the following statement.
London is in England.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
Find the truth value of the following statement.
It is not true that 3 − 7i is a real number.
Find the truth value of the following statement.
Every accountant is free to apply his own accounting rules if and only if machinery is an asset.
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [(~ p ∨ s) ∧ (~ q ∧ r)]
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is not holiday or Ram studies on holiday.
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is a holiday and Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q → p
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The Sun has set and Moon has risen.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If Kiran drives the car, then Sameer will walk.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The drug is effective though it has side effects.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is interesting iff the proof is lengthy.
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
Write the negation of the following statement.
10 > 5 and 3 < 8
Negation of p → (p ˅ ∼ q) is ______
If p → q is an implication, then the implication ∼ q → ∼ p is called its
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form
If Kutab – Minar is in Delhi then Taj - Mahal is in Agra
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)

If p and q are true and rands are false statements, then which of the following is true?
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
Write the negation of p ↔ q.
